MAYBE * Step 1: DependencyPairs MAYBE + Considered Problem: - Strict TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() __(X,nil()) -> X __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0} / {nil/0,tt/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11,U21,U22,U31,U41,U42,U51,U52,U61,U71,U72,U81,__,isList ,isNeList,isNePal,isPal,isQid} and constructors {nil,tt} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs U11#(tt()) -> c_1() U21#(tt()) -> c_2(U22#(isList()),isList#()) U22#(tt()) -> c_3() U31#(tt()) -> c_4() U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U42#(tt()) -> c_6() U51#(tt()) -> c_7(U52#(isList()),isList#()) U52#(tt()) -> c_8() U61#(tt()) -> c_9() U71#(tt()) -> c_10(U72#(isPal()),isPal#()) U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(__(X,Y),Z) -> c_14(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_15() isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isList#() -> c_18() isNeList#() -> c_19(U31#(isQid()),isQid#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) isPal#() -> c_25() isQid#() -> c_26() Weak DPs and mark the set of starting terms. * Step 2: UsableRules MAYBE + Considered Problem: - Strict DPs: U11#(tt()) -> c_1() U21#(tt()) -> c_2(U22#(isList()),isList#()) U22#(tt()) -> c_3() U31#(tt()) -> c_4() U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U42#(tt()) -> c_6() U51#(tt()) -> c_7(U52#(isList()),isList#()) U52#(tt()) -> c_8() U61#(tt()) -> c_9() U71#(tt()) -> c_10(U72#(isPal()),isPal#()) U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(__(X,Y),Z) -> c_14(__#(X,__(Y,Z)),__#(Y,Z)) __#(nil(),X) -> c_15() isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isList#() -> c_18() isNeList#() -> c_19(U31#(isQid()),isQid#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) isPal#() -> c_25() isQid#() -> c_26() - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() __(X,nil()) -> X __(__(X,Y),Z) -> __(X,__(Y,Z)) __(nil(),X) -> X isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2,c_6/0,c_7/2 ,c_8/0,c_9/0,c_10/2,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/2,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/2,c_24/2,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() U11#(tt()) -> c_1() U21#(tt()) -> c_2(U22#(isList()),isList#()) U22#(tt()) -> c_3() U31#(tt()) -> c_4() U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U42#(tt()) -> c_6() U51#(tt()) -> c_7(U52#(isList()),isList#()) U52#(tt()) -> c_8() U61#(tt()) -> c_9() U71#(tt()) -> c_10(U72#(isPal()),isPal#()) U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(nil(),X) -> c_15() isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isList#() -> c_18() isNeList#() -> c_19(U31#(isQid()),isQid#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) isPal#() -> c_25() isQid#() -> c_26() * Step 3: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: U11#(tt()) -> c_1() U21#(tt()) -> c_2(U22#(isList()),isList#()) U22#(tt()) -> c_3() U31#(tt()) -> c_4() U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U42#(tt()) -> c_6() U51#(tt()) -> c_7(U52#(isList()),isList#()) U52#(tt()) -> c_8() U61#(tt()) -> c_9() U71#(tt()) -> c_10(U72#(isPal()),isPal#()) U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(nil(),X) -> c_15() isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isList#() -> c_18() isNeList#() -> c_19(U31#(isQid()),isQid#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) isPal#() -> c_25() isQid#() -> c_26() - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2,c_6/0,c_7/2 ,c_8/0,c_9/0,c_10/2,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/2,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/2,c_24/2,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1,3,4,6,8,9,11,12,13,14,17,24,25} by application of Pre({1,3,4,6,8,9,11,12,13,14,17,24,25}) = {2,5,7,10,15,16,18,19,21,22,23}. Here rules are labelled as follows: 1: U11#(tt()) -> c_1() 2: U21#(tt()) -> c_2(U22#(isList()),isList#()) 3: U22#(tt()) -> c_3() 4: U31#(tt()) -> c_4() 5: U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) 6: U42#(tt()) -> c_6() 7: U51#(tt()) -> c_7(U52#(isList()),isList#()) 8: U52#(tt()) -> c_8() 9: U61#(tt()) -> c_9() 10: U71#(tt()) -> c_10(U72#(isPal()),isPal#()) 11: U72#(tt()) -> c_11() 12: U81#(tt()) -> c_12() 13: __#(X,nil()) -> c_13() 14: __#(nil(),X) -> c_15() 15: isList#() -> c_16(U11#(isNeList()),isNeList#()) 16: isList#() -> c_17(U21#(isList()),isList#()) 17: isList#() -> c_18() 18: isNeList#() -> c_19(U31#(isQid()),isQid#()) 19: isNeList#() -> c_20(U41#(isList()),isList#()) 20: isNeList#() -> c_21(U51#(isNeList()),isNeList#()) 21: isNePal#() -> c_22(U61#(isQid()),isQid#()) 22: isNePal#() -> c_23(U71#(isQid()),isQid#()) 23: isPal#() -> c_24(U81#(isNePal()),isNePal#()) 24: isPal#() -> c_25() 25: isQid#() -> c_26() * Step 4: PredecessorEstimation MAYBE + Considered Problem: - Strict DPs: U21#(tt()) -> c_2(U22#(isList()),isList#()) U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U51#(tt()) -> c_7(U52#(isList()),isList#()) U71#(tt()) -> c_10(U72#(isPal()),isPal#()) isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_19(U31#(isQid()),isQid#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) - Weak DPs: U11#(tt()) -> c_1() U22#(tt()) -> c_3() U31#(tt()) -> c_4() U42#(tt()) -> c_6() U52#(tt()) -> c_8() U61#(tt()) -> c_9() U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(nil(),X) -> c_15() isList#() -> c_18() isPal#() -> c_25() isQid#() -> c_26() - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2,c_6/0,c_7/2 ,c_8/0,c_9/0,c_10/2,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/2,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/2,c_24/2,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {7,10} by application of Pre({7,10}) = {2,5,9,12}. Here rules are labelled as follows: 1: U21#(tt()) -> c_2(U22#(isList()),isList#()) 2: U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) 3: U51#(tt()) -> c_7(U52#(isList()),isList#()) 4: U71#(tt()) -> c_10(U72#(isPal()),isPal#()) 5: isList#() -> c_16(U11#(isNeList()),isNeList#()) 6: isList#() -> c_17(U21#(isList()),isList#()) 7: isNeList#() -> c_19(U31#(isQid()),isQid#()) 8: isNeList#() -> c_20(U41#(isList()),isList#()) 9: isNeList#() -> c_21(U51#(isNeList()),isNeList#()) 10: isNePal#() -> c_22(U61#(isQid()),isQid#()) 11: isNePal#() -> c_23(U71#(isQid()),isQid#()) 12: isPal#() -> c_24(U81#(isNePal()),isNePal#()) 13: U11#(tt()) -> c_1() 14: U22#(tt()) -> c_3() 15: U31#(tt()) -> c_4() 16: U42#(tt()) -> c_6() 17: U52#(tt()) -> c_8() 18: U61#(tt()) -> c_9() 19: U72#(tt()) -> c_11() 20: U81#(tt()) -> c_12() 21: __#(X,nil()) -> c_13() 22: __#(nil(),X) -> c_15() 23: isList#() -> c_18() 24: isPal#() -> c_25() 25: isQid#() -> c_26() * Step 5: RemoveWeakSuffixes MAYBE + Considered Problem: - Strict DPs: U21#(tt()) -> c_2(U22#(isList()),isList#()) U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U51#(tt()) -> c_7(U52#(isList()),isList#()) U71#(tt()) -> c_10(U72#(isPal()),isPal#()) isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) - Weak DPs: U11#(tt()) -> c_1() U22#(tt()) -> c_3() U31#(tt()) -> c_4() U42#(tt()) -> c_6() U52#(tt()) -> c_8() U61#(tt()) -> c_9() U72#(tt()) -> c_11() U81#(tt()) -> c_12() __#(X,nil()) -> c_13() __#(nil(),X) -> c_15() isList#() -> c_18() isNeList#() -> c_19(U31#(isQid()),isQid#()) isNePal#() -> c_22(U61#(isQid()),isQid#()) isPal#() -> c_25() isQid#() -> c_26() - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2,c_6/0,c_7/2 ,c_8/0,c_9/0,c_10/2,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/2,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/2,c_24/2,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: RemoveWeakSuffixes + Details: Consider the dependency graph 1:S:U21#(tt()) -> c_2(U22#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_2 isList#() -> c_18():21 -->_1 U22#(tt()) -> c_3():12 2:S:U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_19(U31#(isQid()),isQid#()):22 -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 -->_1 U42#(tt()) -> c_6():14 3:S:U51#(tt()) -> c_7(U52#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_2 isList#() -> c_18():21 -->_1 U52#(tt()) -> c_8():15 4:S:U71#(tt()) -> c_10(U72#(isPal()),isPal#()) -->_2 isPal#() -> c_24(U81#(isNePal()),isNePal#()):10 -->_2 isPal#() -> c_25():24 -->_1 U72#(tt()) -> c_11():17 5:S:isList#() -> c_16(U11#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_19(U31#(isQid()),isQid#()):22 -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 -->_1 U11#(tt()) -> c_1():11 6:S:isList#() -> c_17(U21#(isList()),isList#()) -->_2 isList#() -> c_18():21 -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_1 U21#(tt()) -> c_2(U22#(isList()),isList#()):1 7:S:isNeList#() -> c_20(U41#(isList()),isList#()) -->_2 isList#() -> c_18():21 -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_1 U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()):2 8:S:isNeList#() -> c_21(U51#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_19(U31#(isQid()),isQid#()):22 -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 -->_1 U51#(tt()) -> c_7(U52#(isList()),isList#()):3 9:S:isNePal#() -> c_23(U71#(isQid()),isQid#()) -->_2 isQid#() -> c_26():25 -->_1 U71#(tt()) -> c_10(U72#(isPal()),isPal#()):4 10:S:isPal#() -> c_24(U81#(isNePal()),isNePal#()) -->_2 isNePal#() -> c_22(U61#(isQid()),isQid#()):23 -->_1 U81#(tt()) -> c_12():18 -->_2 isNePal#() -> c_23(U71#(isQid()),isQid#()):9 11:W:U11#(tt()) -> c_1() 12:W:U22#(tt()) -> c_3() 13:W:U31#(tt()) -> c_4() 14:W:U42#(tt()) -> c_6() 15:W:U52#(tt()) -> c_8() 16:W:U61#(tt()) -> c_9() 17:W:U72#(tt()) -> c_11() 18:W:U81#(tt()) -> c_12() 19:W:__#(X,nil()) -> c_13() 20:W:__#(nil(),X) -> c_15() 21:W:isList#() -> c_18() 22:W:isNeList#() -> c_19(U31#(isQid()),isQid#()) -->_2 isQid#() -> c_26():25 -->_1 U31#(tt()) -> c_4():13 23:W:isNePal#() -> c_22(U61#(isQid()),isQid#()) -->_2 isQid#() -> c_26():25 -->_1 U61#(tt()) -> c_9():16 24:W:isPal#() -> c_25() 25:W:isQid#() -> c_26() The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed. 20: __#(nil(),X) -> c_15() 19: __#(X,nil()) -> c_13() 17: U72#(tt()) -> c_11() 24: isPal#() -> c_25() 18: U81#(tt()) -> c_12() 23: isNePal#() -> c_22(U61#(isQid()),isQid#()) 16: U61#(tt()) -> c_9() 12: U22#(tt()) -> c_3() 11: U11#(tt()) -> c_1() 15: U52#(tt()) -> c_8() 14: U42#(tt()) -> c_6() 22: isNeList#() -> c_19(U31#(isQid()),isQid#()) 13: U31#(tt()) -> c_4() 25: isQid#() -> c_26() 21: isList#() -> c_18() * Step 6: SimplifyRHS MAYBE + Considered Problem: - Strict DPs: U21#(tt()) -> c_2(U22#(isList()),isList#()) U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) U51#(tt()) -> c_7(U52#(isList()),isList#()) U71#(tt()) -> c_10(U72#(isPal()),isPal#()) isList#() -> c_16(U11#(isNeList()),isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid()),isQid#()) isPal#() -> c_24(U81#(isNePal()),isNePal#()) - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/2,c_3/0,c_4/0,c_5/2,c_6/0,c_7/2 ,c_8/0,c_9/0,c_10/2,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/2,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/2,c_24/2,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:U21#(tt()) -> c_2(U22#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 2:S:U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 3:S:U51#(tt()) -> c_7(U52#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 4:S:U71#(tt()) -> c_10(U72#(isPal()),isPal#()) -->_2 isPal#() -> c_24(U81#(isNePal()),isNePal#()):10 5:S:isList#() -> c_16(U11#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 6:S:isList#() -> c_17(U21#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_1 U21#(tt()) -> c_2(U22#(isList()),isList#()):1 7:S:isNeList#() -> c_20(U41#(isList()),isList#()) -->_2 isList#() -> c_17(U21#(isList()),isList#()):6 -->_2 isList#() -> c_16(U11#(isNeList()),isNeList#()):5 -->_1 U41#(tt()) -> c_5(U42#(isNeList()),isNeList#()):2 8:S:isNeList#() -> c_21(U51#(isNeList()),isNeList#()) -->_2 isNeList#() -> c_21(U51#(isNeList()),isNeList#()):8 -->_2 isNeList#() -> c_20(U41#(isList()),isList#()):7 -->_1 U51#(tt()) -> c_7(U52#(isList()),isList#()):3 9:S:isNePal#() -> c_23(U71#(isQid()),isQid#()) -->_1 U71#(tt()) -> c_10(U72#(isPal()),isPal#()):4 10:S:isPal#() -> c_24(U81#(isNePal()),isNePal#()) -->_2 isNePal#() -> c_23(U71#(isQid()),isQid#()):9 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isList#() -> c_16(isNeList#()) isNePal#() -> c_23(U71#(isQid())) isPal#() -> c_24(isNePal#()) * Step 7: UsableRules MAYBE + Considered Problem: - Strict DPs: U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isList#() -> c_16(isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid())) isPal#() -> c_24(isNePal#()) - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() U61(tt()) -> tt() U71(tt()) -> U72(isPal()) U72(tt()) -> tt() U81(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isNePal() -> U61(isQid()) isNePal() -> U71(isQid()) isPal() -> U81(isNePal()) isPal() -> tt() isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1 ,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/1,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/1,c_24/1,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isQid() -> tt() U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isList#() -> c_16(isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid())) isPal#() -> c_24(isNePal#()) * Step 8: WeightGap MAYBE + Considered Problem: - Strict DPs: U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isList#() -> c_16(isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid())) isPal#() -> c_24(isNePal#()) - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1 ,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/1,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/1,c_24/1,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(U11) = {1}, uargs(U21) = {1}, uargs(U22) = {1}, uargs(U31) = {1}, uargs(U41) = {1}, uargs(U42) = {1}, uargs(U51) = {1}, uargs(U52) = {1}, uargs(U21#) = {1}, uargs(U41#) = {1}, uargs(U51#) = {1}, uargs(U71#) = {1}, uargs(c_2) = {1}, uargs(c_5) = {1}, uargs(c_7) = {1}, uargs(c_10) = {1}, uargs(c_16) = {1}, uargs(c_17) = {1,2}, uargs(c_20) = {1,2}, uargs(c_21) = {1,2}, uargs(c_23) = {1}, uargs(c_24) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(U11) = [1] x1 + [0] p(U21) = [1] x1 + [0] p(U22) = [1] x1 + [0] p(U31) = [1] x1 + [0] p(U41) = [1] x1 + [0] p(U42) = [1] x1 + [0] p(U51) = [1] x1 + [0] p(U52) = [1] x1 + [0] p(U61) = [0] p(U71) = [0] p(U72) = [0] p(U81) = [0] p(__) = [0] p(isList) = [6] p(isNeList) = [6] p(isNePal) = [0] p(isPal) = [1] p(isQid) = [6] p(nil) = [0] p(tt) = [6] p(U11#) = [1] p(U21#) = [1] x1 + [0] p(U22#) = [0] p(U31#) = [0] p(U41#) = [1] x1 + [0] p(U42#) = [0] p(U51#) = [1] x1 + [0] p(U52#) = [0] p(U61#) = [0] p(U71#) = [1] x1 + [0] p(U72#) = [0] p(U81#) = [0] p(__#) = [0] p(isList#) = [0] p(isNeList#) = [0] p(isNePal#) = [0] p(isPal#) = [1] p(isQid#) = [0] p(c_1) = [0] p(c_2) = [1] x1 + [0] p(c_3) = [0] p(c_4) = [0] p(c_5) = [1] x1 + [0] p(c_6) = [0] p(c_7) = [1] x1 + [0] p(c_8) = [0] p(c_9) = [0] p(c_10) = [1] x1 + [0] p(c_11) = [0] p(c_12) = [0] p(c_13) = [0] p(c_14) = [0] p(c_15) = [0] p(c_16) = [1] x1 + [0] p(c_17) = [1] x1 + [1] x2 + [0] p(c_18) = [0] p(c_19) = [0] p(c_20) = [1] x1 + [1] x2 + [0] p(c_21) = [1] x1 + [1] x2 + [0] p(c_22) = [0] p(c_23) = [1] x1 + [0] p(c_24) = [1] x1 + [0] p(c_25) = [0] p(c_26) = [0] Following rules are strictly oriented: U21#(tt()) = [6] > [0] = c_2(isList#()) U41#(tt()) = [6] > [0] = c_5(isNeList#()) U51#(tt()) = [6] > [0] = c_7(isList#()) U71#(tt()) = [6] > [1] = c_10(isPal#()) isPal#() = [1] > [0] = c_24(isNePal#()) Following rules are (at-least) weakly oriented: isList#() = [0] >= [0] = c_16(isNeList#()) isList#() = [0] >= [6] = c_17(U21#(isList()),isList#()) isNeList#() = [0] >= [6] = c_20(U41#(isList()),isList#()) isNeList#() = [0] >= [6] = c_21(U51#(isNeList()),isNeList#()) isNePal#() = [0] >= [6] = c_23(U71#(isQid())) U11(tt()) = [6] >= [6] = tt() U21(tt()) = [6] >= [6] = U22(isList()) U22(tt()) = [6] >= [6] = tt() U31(tt()) = [6] >= [6] = tt() U41(tt()) = [6] >= [6] = U42(isNeList()) U42(tt()) = [6] >= [6] = tt() U51(tt()) = [6] >= [6] = U52(isList()) U52(tt()) = [6] >= [6] = tt() isList() = [6] >= [6] = U11(isNeList()) isList() = [6] >= [6] = U21(isList()) isList() = [6] >= [6] = tt() isNeList() = [6] >= [6] = U31(isQid()) isNeList() = [6] >= [6] = U41(isList()) isNeList() = [6] >= [6] = U51(isNeList()) isQid() = [6] >= [6] = tt() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 9: WeightGap MAYBE + Considered Problem: - Strict DPs: isList#() -> c_16(isNeList#()) isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid())) - Weak DPs: U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isPal#() -> c_24(isNePal#()) - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1 ,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/1,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/1,c_24/1,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(U11) = {1}, uargs(U21) = {1}, uargs(U22) = {1}, uargs(U31) = {1}, uargs(U41) = {1}, uargs(U42) = {1}, uargs(U51) = {1}, uargs(U52) = {1}, uargs(U21#) = {1}, uargs(U41#) = {1}, uargs(U51#) = {1}, uargs(U71#) = {1}, uargs(c_2) = {1}, uargs(c_5) = {1}, uargs(c_7) = {1}, uargs(c_10) = {1}, uargs(c_16) = {1}, uargs(c_17) = {1,2}, uargs(c_20) = {1,2}, uargs(c_21) = {1,2}, uargs(c_23) = {1}, uargs(c_24) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(U11) = [1] x1 + [0] p(U21) = [1] x1 + [0] p(U22) = [1] x1 + [0] p(U31) = [1] x1 + [0] p(U41) = [1] x1 + [0] p(U42) = [1] x1 + [0] p(U51) = [1] x1 + [0] p(U52) = [1] x1 + [0] p(U61) = [0] p(U71) = [0] p(U72) = [0] p(U81) = [0] p(__) = [0] p(isList) = [2] p(isNeList) = [2] p(isNePal) = [0] p(isPal) = [0] p(isQid) = [2] p(nil) = [0] p(tt) = [2] p(U11#) = [0] p(U21#) = [1] x1 + [0] p(U22#) = [0] p(U31#) = [0] p(U41#) = [1] x1 + [5] p(U42#) = [0] p(U51#) = [1] x1 + [1] p(U52#) = [0] p(U61#) = [0] p(U71#) = [1] x1 + [0] p(U72#) = [0] p(U81#) = [0] p(__#) = [2] x2 + [0] p(isList#) = [1] p(isNeList#) = [0] p(isNePal#) = [0] p(isPal#) = [1] p(isQid#) = [1] p(c_1) = [0] p(c_2) = [1] x1 + [0] p(c_3) = [2] p(c_4) = [1] p(c_5) = [1] x1 + [2] p(c_6) = [1] p(c_7) = [1] x1 + [1] p(c_8) = [0] p(c_9) = [0] p(c_10) = [1] x1 + [0] p(c_11) = [0] p(c_12) = [0] p(c_13) = [0] p(c_14) = [2] x2 + [0] p(c_15) = [1] p(c_16) = [1] x1 + [0] p(c_17) = [1] x1 + [1] x2 + [4] p(c_18) = [2] p(c_19) = [1] x1 + [1] x2 + [2] p(c_20) = [1] x1 + [1] x2 + [0] p(c_21) = [1] x1 + [1] x2 + [0] p(c_22) = [8] x1 + [8] x2 + [1] p(c_23) = [1] x1 + [0] p(c_24) = [1] x1 + [0] p(c_25) = [2] p(c_26) = [1] Following rules are strictly oriented: isList#() = [1] > [0] = c_16(isNeList#()) Following rules are (at-least) weakly oriented: U21#(tt()) = [2] >= [1] = c_2(isList#()) U41#(tt()) = [7] >= [2] = c_5(isNeList#()) U51#(tt()) = [3] >= [2] = c_7(isList#()) U71#(tt()) = [2] >= [1] = c_10(isPal#()) isList#() = [1] >= [7] = c_17(U21#(isList()),isList#()) isNeList#() = [0] >= [8] = c_20(U41#(isList()),isList#()) isNeList#() = [0] >= [3] = c_21(U51#(isNeList()),isNeList#()) isNePal#() = [0] >= [2] = c_23(U71#(isQid())) isPal#() = [1] >= [0] = c_24(isNePal#()) U11(tt()) = [2] >= [2] = tt() U21(tt()) = [2] >= [2] = U22(isList()) U22(tt()) = [2] >= [2] = tt() U31(tt()) = [2] >= [2] = tt() U41(tt()) = [2] >= [2] = U42(isNeList()) U42(tt()) = [2] >= [2] = tt() U51(tt()) = [2] >= [2] = U52(isList()) U52(tt()) = [2] >= [2] = tt() isList() = [2] >= [2] = U11(isNeList()) isList() = [2] >= [2] = U21(isList()) isList() = [2] >= [2] = tt() isNeList() = [2] >= [2] = U31(isQid()) isNeList() = [2] >= [2] = U41(isList()) isNeList() = [2] >= [2] = U51(isNeList()) isQid() = [2] >= [2] = tt() Further, it can be verified that all rules not oriented are covered by the weightgap condition. * Step 10: Failure MAYBE + Considered Problem: - Strict DPs: isList#() -> c_17(U21#(isList()),isList#()) isNeList#() -> c_20(U41#(isList()),isList#()) isNeList#() -> c_21(U51#(isNeList()),isNeList#()) isNePal#() -> c_23(U71#(isQid())) - Weak DPs: U21#(tt()) -> c_2(isList#()) U41#(tt()) -> c_5(isNeList#()) U51#(tt()) -> c_7(isList#()) U71#(tt()) -> c_10(isPal#()) isList#() -> c_16(isNeList#()) isPal#() -> c_24(isNePal#()) - Weak TRS: U11(tt()) -> tt() U21(tt()) -> U22(isList()) U22(tt()) -> tt() U31(tt()) -> tt() U41(tt()) -> U42(isNeList()) U42(tt()) -> tt() U51(tt()) -> U52(isList()) U52(tt()) -> tt() isList() -> U11(isNeList()) isList() -> U21(isList()) isList() -> tt() isNeList() -> U31(isQid()) isNeList() -> U41(isList()) isNeList() -> U51(isNeList()) isQid() -> tt() - Signature: {U11/1,U21/1,U22/1,U31/1,U41/1,U42/1,U51/1,U52/1,U61/1,U71/1,U72/1,U81/1,__/2,isList/0,isNeList/0,isNePal/0 ,isPal/0,isQid/0,U11#/1,U21#/1,U22#/1,U31#/1,U41#/1,U42#/1,U51#/1,U52#/1,U61#/1,U71#/1,U72#/1,U81#/1,__#/2 ,isList#/0,isNeList#/0,isNePal#/0,isPal#/0,isQid#/0} / {nil/0,tt/0,c_1/0,c_2/1,c_3/0,c_4/0,c_5/1,c_6/0,c_7/1 ,c_8/0,c_9/0,c_10/1,c_11/0,c_12/0,c_13/0,c_14/2,c_15/0,c_16/1,c_17/2,c_18/0,c_19/2,c_20/2,c_21/2,c_22/2 ,c_23/1,c_24/1,c_25/0,c_26/0} - Obligation: innermost runtime complexity wrt. defined symbols {U11#,U21#,U22#,U31#,U41#,U42#,U51#,U52#,U61#,U71#,U72# ,U81#,__#,isList#,isNeList#,isNePal#,isPal#,isQid#} and constructors {nil,tt} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE