MAYBE * Step 1: InnermostRuleRemoval MAYBE + Considered Problem: - Strict TRS: b(y,z) -> f(c(c(y,z,z),a(),a())) b(b(z,y),a()) -> z c(f(z),f(c(a(),x,a())),y) -> c(f(b(x,z)),c(z,y,a()),a()) - Signature: {b/2,c/3} / {a/0,f/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c} and constructors {a,f} + Applied Processor: InnermostRuleRemoval + Details: Arguments of following rules are not normal-forms. b(b(z,y),a()) -> z All above mentioned rules can be savely removed. * Step 2: DependencyPairs MAYBE + Considered Problem: - Strict TRS: b(y,z) -> f(c(c(y,z,z),a(),a())) c(f(z),f(c(a(),x,a())),y) -> c(f(b(x,z)),c(z,y,a()),a()) - Signature: {b/2,c/3} / {a/0,f/1} - Obligation: innermost runtime complexity wrt. defined symbols {b,c} and constructors {a,f} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs b#(y,z) -> c_1(c#(c(y,z,z),a(),a()),c#(y,z,z)) c#(f(z),f(c(a(),x,a())),y) -> c_2(c#(f(b(x,z)),c(z,y,a()),a()),b#(x,z),c#(z,y,a())) Weak DPs and mark the set of starting terms. * Step 3: Failure MAYBE + Considered Problem: - Strict DPs: b#(y,z) -> c_1(c#(c(y,z,z),a(),a()),c#(y,z,z)) c#(f(z),f(c(a(),x,a())),y) -> c_2(c#(f(b(x,z)),c(z,y,a()),a()),b#(x,z),c#(z,y,a())) - Weak TRS: b(y,z) -> f(c(c(y,z,z),a(),a())) c(f(z),f(c(a(),x,a())),y) -> c(f(b(x,z)),c(z,y,a()),a()) - Signature: {b/2,c/3,b#/2,c#/3} / {a/0,f/1,c_1/2,c_2/3} - Obligation: innermost runtime complexity wrt. defined symbols {b#,c#} and constructors {a,f} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE