MAYBE * Step 1: DependencyPairs MAYBE + Considered Problem: - Strict TRS: f(x,y,g(z)) -> g(f(x,y,z)) f(x,g(y),z) -> g(f(x,y,z)) f(0(),1(),x) -> f(g(x),g(x),x) f(g(x),y,z) -> g(f(x,y,z)) - Signature: {f/3} / {0/0,1/0,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,1,g} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs f#(x,y,g(z)) -> c_1(f#(x,y,z)) f#(x,g(y),z) -> c_2(f#(x,y,z)) f#(0(),1(),x) -> c_3(f#(g(x),g(x),x)) f#(g(x),y,z) -> c_4(f#(x,y,z)) Weak DPs and mark the set of starting terms. * Step 2: UsableRules MAYBE + Considered Problem: - Strict DPs: f#(x,y,g(z)) -> c_1(f#(x,y,z)) f#(x,g(y),z) -> c_2(f#(x,y,z)) f#(0(),1(),x) -> c_3(f#(g(x),g(x),x)) f#(g(x),y,z) -> c_4(f#(x,y,z)) - Weak TRS: f(x,y,g(z)) -> g(f(x,y,z)) f(x,g(y),z) -> g(f(x,y,z)) f(0(),1(),x) -> f(g(x),g(x),x) f(g(x),y,z) -> g(f(x,y,z)) - Signature: {f/3,f#/3} / {0/0,1/0,g/1,c_1/1,c_2/1,c_3/1,c_4/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {0,1,g} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(x,y,g(z)) -> c_1(f#(x,y,z)) f#(x,g(y),z) -> c_2(f#(x,y,z)) f#(0(),1(),x) -> c_3(f#(g(x),g(x),x)) f#(g(x),y,z) -> c_4(f#(x,y,z)) * Step 3: Failure MAYBE + Considered Problem: - Strict DPs: f#(x,y,g(z)) -> c_1(f#(x,y,z)) f#(x,g(y),z) -> c_2(f#(x,y,z)) f#(0(),1(),x) -> c_3(f#(g(x),g(x),x)) f#(g(x),y,z) -> c_4(f#(x,y,z)) - Signature: {f/3,f#/3} / {0/0,1/0,g/1,c_1/1,c_2/1,c_3/1,c_4/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {0,1,g} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE