5.15/2.15	YES
5.15/2.17	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
5.15/2.17	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
5.15/2.17	
5.15/2.17	
5.15/2.17	Termination of the given RelTRS could be proven:
5.15/2.17	
5.15/2.17	(0) RelTRS
5.15/2.17	(1) RelTRS S Cleaner [EQUIVALENT, 0 ms]
5.15/2.17	(2) RelTRS
5.15/2.17	(3) RelTRSRRRProof [EQUIVALENT, 82 ms]
5.15/2.17	(4) RelTRS
5.15/2.17	(5) RelTRSRRRProof [EQUIVALENT, 11 ms]
5.15/2.17	(6) RelTRS
5.15/2.17	(7) RelTRSRRRProof [EQUIVALENT, 10 ms]
5.15/2.17	(8) RelTRS
5.15/2.17	(9) RIsEmptyProof [EQUIVALENT, 0 ms]
5.15/2.17	(10) YES
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(0)
5.15/2.17	Obligation:
5.15/2.17	Relative term rewrite system:
5.15/2.17	The relative TRS consists of the following R rules:
5.15/2.17	
5.15/2.17	   topB(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	   topA(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topB(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topA(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	
5.15/2.17	The relative TRS consists of the following S rules:
5.15/2.17	
5.15/2.17	   topA(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topA(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	   topA(i, N1(x), y) -> topA(i, N1(C(x)), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(i, x, N2(C(y)))
5.15/2.17	   topA(i, T1(x), y) -> topA(i, T1(x), y)
5.15/2.17	   topB(i, x, T2(y)) -> topB(i, x, T2(y))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, S2(D(y)))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(1) RelTRS S Cleaner (EQUIVALENT)
5.15/2.17	We have deleted all rules from S that have the shape t -> t:
5.15/2.17	
5.15/2.17	   topA(i, T1(x), y) -> topA(i, T1(x), y)
5.15/2.17	   topB(i, x, T2(y)) -> topB(i, x, T2(y))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(2)
5.15/2.17	Obligation:
5.15/2.17	Relative term rewrite system:
5.15/2.17	The relative TRS consists of the following R rules:
5.15/2.17	
5.15/2.17	   topB(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	   topA(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topB(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topA(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	
5.15/2.17	The relative TRS consists of the following S rules:
5.15/2.17	
5.15/2.17	   topA(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topA(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	   topA(i, N1(x), y) -> topA(i, N1(C(x)), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(i, x, N2(C(y)))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, S2(D(y)))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(3) RelTRSRRRProof (EQUIVALENT)
5.15/2.17	We used the following monotonic ordering for rule removal:
5.15/2.17	Polynomial interpretation [POLO]:
5.15/2.17	
5.15/2.17	   POL(0) = 0
5.15/2.17	   POL(1) = 0
5.15/2.17	   POL(C(x_1)) = x_1
5.15/2.17	   POL(D(x_1)) = x_1
5.15/2.17	   POL(N1(x_1)) = 1 + x_1
5.15/2.17	   POL(N2(x_1)) = x_1
5.15/2.17	   POL(S1(x_1)) = 1 + x_1
5.15/2.17	   POL(S2(x_1)) = x_1
5.15/2.17	   POL(T1(x_1)) = x_1
5.15/2.17	   POL(T2(x_1)) = x_1
5.15/2.17	   POL(topA(x_1, x_2, x_3)) = x_1 + x_2 + x_3
5.15/2.17	   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
5.15/2.17	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.15/2.17	Rules from R:
5.15/2.17	
5.15/2.17	   topB(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	Rules from S:
5.15/2.17	
5.15/2.17	   topA(i, N1(x), y) -> topA(1, T1(x), y)
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(4)
5.15/2.17	Obligation:
5.15/2.17	Relative term rewrite system:
5.15/2.17	The relative TRS consists of the following R rules:
5.15/2.17	
5.15/2.17	   topA(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topB(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topA(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	
5.15/2.17	The relative TRS consists of the following S rules:
5.15/2.17	
5.15/2.17	   topB(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topA(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	   topA(i, N1(x), y) -> topA(i, N1(C(x)), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(i, x, N2(C(y)))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, S2(D(y)))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(5) RelTRSRRRProof (EQUIVALENT)
5.15/2.17	We used the following monotonic ordering for rule removal:
5.15/2.17	Polynomial interpretation [POLO]:
5.15/2.17	
5.15/2.17	   POL(0) = 0
5.15/2.17	   POL(1) = 0
5.15/2.17	   POL(C(x_1)) = x_1
5.15/2.17	   POL(D(x_1)) = x_1
5.15/2.17	   POL(N1(x_1)) = x_1
5.15/2.17	   POL(N2(x_1)) = x_1
5.15/2.17	   POL(S1(x_1)) = 1 + x_1
5.15/2.17	   POL(S2(x_1)) = x_1
5.15/2.17	   POL(T1(x_1)) = x_1
5.15/2.17	   POL(T2(x_1)) = x_1
5.15/2.17	   POL(topA(x_1, x_2, x_3)) = x_1 + x_2 + x_3
5.15/2.17	   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
5.15/2.17	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.15/2.17	Rules from R:
5.15/2.17	
5.15/2.17	   topB(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	Rules from S:
5.15/2.17	
5.15/2.17	   topA(i, S1(x), y) -> topA(i, N1(x), y)
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(6)
5.15/2.17	Obligation:
5.15/2.17	Relative term rewrite system:
5.15/2.17	The relative TRS consists of the following R rules:
5.15/2.17	
5.15/2.17	   topA(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topA(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	
5.15/2.17	The relative TRS consists of the following S rules:
5.15/2.17	
5.15/2.17	   topB(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	   topA(i, N1(x), y) -> topA(i, N1(C(x)), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(i, x, N2(C(y)))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, S2(D(y)))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(7) RelTRSRRRProof (EQUIVALENT)
5.15/2.17	We used the following monotonic ordering for rule removal:
5.15/2.17	Polynomial interpretation [POLO]:
5.15/2.17	
5.15/2.17	   POL(0) = 0
5.15/2.17	   POL(1) = 0
5.15/2.17	   POL(C(x_1)) = x_1
5.15/2.17	   POL(D(x_1)) = x_1
5.15/2.17	   POL(N1(x_1)) = x_1
5.15/2.17	   POL(N2(x_1)) = x_1
5.15/2.17	   POL(S2(x_1)) = x_1
5.15/2.17	   POL(T1(x_1)) = x_1
5.15/2.17	   POL(T2(x_1)) = x_1
5.15/2.17	   POL(topA(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
5.15/2.17	   POL(topB(x_1, x_2, x_3)) = x_1 + x_2 + x_3
5.15/2.17	With this ordering the following rules can be removed [MATRO] because they are oriented strictly:
5.15/2.17	Rules from R:
5.15/2.17	
5.15/2.17	   topA(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topA(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topA(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topA(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	Rules from S:
5.15/2.17	none
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(8)
5.15/2.17	Obligation:
5.15/2.17	Relative term rewrite system:
5.15/2.17	R is empty.
5.15/2.17	The relative TRS consists of the following S rules:
5.15/2.17	
5.15/2.17	   topB(i, x, N2(y)) -> topB(0, x, T2(y))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, N2(y))
5.15/2.17	   topB(i, N1(x), T2(y)) -> topB(i, N1(x), S2(y))
5.15/2.17	   topB(1, T1(x), T2(y)) -> topB(1, T1(x), S2(y))
5.15/2.17	   topA(i, N1(x), y) -> topA(i, N1(C(x)), y)
5.15/2.17	   topB(i, x, N2(y)) -> topB(i, x, N2(C(y)))
5.15/2.17	   topB(i, x, S2(y)) -> topB(i, x, S2(D(y)))
5.15/2.17	
5.15/2.17	
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(9) RIsEmptyProof (EQUIVALENT)
5.15/2.17	The TRS R is empty. Hence, termination is trivially proven.
5.15/2.17	----------------------------------------
5.15/2.17	
5.15/2.17	(10)
5.15/2.17	YES
5.59/2.28	EOF